1
1
DIGITAL TECHNICS
Dr. Bálint Pődör
Óbuda University,
Microelectronics and Technology Institute
1. LECTURE:
COMBINATONAL CIRCUITS BASIC CONCEPTS
2016/2017
2
1. LECTURE: COMBINATONAL CIRCUITS
BASIC CONCEPTS
1. General introduction to the course
2. Combinational circuits: basic concepts
3. Boolean algebra and logic functions: a review
Comment:
These files are based on the lectures presented during the
first (Autumn) term of the 2016/2017 educational year.
2
3
AIMS AND SCOPE
This course will give an overview of the basic concepts and
applications of digital technics, from Boolean algebra to
microprocessors.
The lectures will cover more advanced materials and subjects
than those contained the introductory three semester course
of the B.Sc. programme. It will focus more on the general
concepts of the subject and less on the practical details.
In this respect it is supposed that the students have already a
good foundation and a certain level of hands-on experience in
digital technics and electronics.
4
TOPICS IN FOCUS
Basic concepts of digital technics
Programmable Logic Devices (PLDs) and Field
Programmable Gate Arrays (FGPAs)
Digital (combinational) design and synthesis
Synchronous sequential circuits analysis and synthesis
Arithmetic circuits, adders and multipliers
MOS, CMOS and VLSI digital circuits.
3
5
A SHORT INTRODUCTION TO
DIGITAL CIRCUITS AND SYSTEMS
A SHORT INTRODUCTION TO DIGITAL
CIRCUITS AND NETWORKS
Digital electronics can be found in many applications in the
form of microprocessors, microcontrollers, PCs, and an
uncountable number of other systems. The design of digital
circuits has progressed from resistor-transistor logic (RTL)
and diode-transistor logic (DTL) to transistor-transistor logic
(TTL) and emitter-coupled logic (ECL) to complementary
metal-oxide-semiconductor (CMOS) logic circuits.
The density and number of transistors in microprocessors
has increased from 2300 in the 1971 4-bit 4004 micro-
processor to 25 million in the more recent IA-64 chip and it
has been reached over one billion transistors by 2010.
4
A SHORT INTRODUCTION TO DIGITAL
CIRCUITS AND NETWORKS
The change that has enabled the widespread economical
use of digital logic has been a dramatic evolution in
device technology, which is most spectacularly described
by Moore`s law. Logic circuits comprising of several basic
electronic devices (typically transistors, resistors, and
diodes), were once designed with each device as a
separate physical entity.
Now, very large-scale integration of devices offers up to
several thousand or even millions of equivalent basic
devices on the surface of a small piece of silicon wafer,
typically rectangular with a maximum dimension of a few
tens of millimeters per side.
MOORE’S LAW
Gordon Moore (co-founder of Intel) predicted in 1965, just four
years after the first planar integrated circuit was discovered, that
the number of transistors per integrated circuit would double
every 18 months.
He forecast that this trend would continue through 1975.
Moore's Law has been
maintained for far longer,
it has become a universal
law of the entire semi-
conductor industry. It still
holds true as we enter the
second decade of new
century.
Moore’s law is about
human ingenuity not physics.
5
MOORE’S LAW
Robert NOYCE the visionary
Gordon MOORE the virtuoso of technology
Andrew GROVE (GRÓF András) the technologist turned scientist
Logic technology node and transistor gate length versus calendar year.
Note:
mainstream Si technology is nanotechnology.
The INTEL’s gurus: A. Groove, R. Noyce
G. Moore INTEL,1970
A SHORT INTRODUCTION TO DIGITAL
CIRCUITS AND NETWORKS
The dramatic reduction in size has been accompanied by
a number of effects. The power consumption and cost per
logic device have been greatly reduced. The cheap digital
watch or the basic electronic calculators that can run for
over a year on tiny battery, or the recent laptop computers
having an affordable price, exemplify these effects.
6
11
COMBINATIONAL CIRCUITS:
AN INTRODUCTION
WITH EXAMPLES
DIGITAL NETWORKS: CLASSIFICATION
Digital/logic circuits/networks can be classified into two
groups:
1. Combinational logic networks
Results of an operation depend only on the present inputs to
the operation
Uses: perform arithmetic, control data movement, compare
values for decision making
2. Sequential logic networks
Results depend on both the inputs to the operation and the
result of the previous operation
Uses: counter, controllers, etc.
7
13
COMBINATIONAL CIRCUITS:
GENERALIZED MODEL AND PROPERTIES
The combinational circuit maps an input (signal) combination
to an output (signal) combination.
A combinational circuit is a circuit with no ”memory”.
The same input combination always implies the very same
output combination (except transients).
The reverse is not true. For a given output combination
different input combinations can belong.
Combinational
circuit
Yi = Fi (A, B, ..., N) i = 1, 2, ... M
Black-box model of combinational circuits.
14
EXAMPLE: 1-BIT FULL ADDER
• Its function is to add two bits and the carry from the
previous position, and to generate the sum and the carry
A
Cin
S
Cout
Full adder B
The full adder as a combinational logic circuit will be used
throughout in these lectures as vehicle to demonstrate and
explain various concepts in digital logic
S = S(A,B,Cin) Cout = C(A,B,Cin)
8
15
FULL ADDER: BOOLEAN FUNCTIONS
Sum
_ _ _ _ _ _
Si = AiBiCi-1 + AiBiCi-1 + AiBiCi-1 + AiBiCi-1
Carry _ _ _
Ci = AiBiCi-1 + AiBiCi-1 + AiBiCi-1 + AiBiCi-1
= AiBi + AiCi-1 + BiCi-1
The sum can be expressed as a three-variable exclusive OR
function (Si = AiBiCi).
The carry is the three-variable majority function and can also
be expressed in various other algebraic forms.
16
ON THE IMPLEMENTATION
OF THE FULL ADDER
A possible technique for implementing the 1-bit full adder is
to generate the two relevant logic function directly
_ _ _ _ _ _
Si = AiBiCi-1 + AiBiCi-1 + AiBiCi-1 + AiBiCi-1
Ci = AiBi + AiCi-1 + BiCi-1
Both require a two level AND-OR circuitry, therefore the time
required to achieve the sum and the carry is equal to the
propagation delay of two gates, or 2 tpd.
An other possibility is to generate the sum using XOR gates.
9
1-BIT FULL ADDER IMPLEMENTATIONS
17
(d)
(e)
(f)
(g)
xi
yi
ci-1
00001111
00110011
01010101
00010111
01101001
ci
si
FA
xi
yi
ci s
i
ci-1
si
ci
ci-1
yi
xi
ci-1
yi
xi
si
18
FULL ADDER: GENERAL RELEVANCE
The full adder is the fundamental building block in many
arithmetic circuits, such as adders and multipliers.
Since these circuits strongly affect the overall performance
in current digital ICs, their speed optimization is crucial in
high performance applications, and typical applications
require a tradeoff between power consumption and speed.
In addition, as arithmetic circuits significantly contribute to
the overall power budget, their power consumption
reduction becomes the main objective to pursue in low-
power ICs used in portable electronic equipment.
10
FULL ADDER IMPLEMENTED IN CMOS
The simplest forms of the sum and carry function are
(written in a form appropriate to CMOS implementation)
_ _ _ _ _
S = C(A B + A B) + C(A B + A B)
Cout = A B + C(A + B)
This is easily implemented using standard CMOS
principles. The total transistor count is 34.
The disadvantage is that the circuit uses the negated
values of the inputs too.
FULL ADDER IMPLEMENTED IN CMOS
This disadvantage can be avoided, if the negated value
of the generated carry Cout is used to calculate the sum
according to
Cout = A B + C(A + B)
___
S = (A + B +C )Cout + A B C
In this case the time delay of the sum will be larger,
because three inverting operation is performed, but this
is not relevant in a parallel (ripple-carry) adder, because
the time necessary for a multi-bit addition is determined
by the propagation time of the carry.
11
CMOS FULL ADDER LOGIC DIAGRAM
21
Cout = A B + C(A + B)
__
S = (A + B +C )Cout + A B C
STATIC 28-T CMOS FULL ADDER
28 transistors
A B
B
A
Ci
Ci A
X
VDD
VDD
A B
Ci BA
B VDD
A
B
Ci
Ci
A
B
A CiB
Co
VDD
S
Cout = A B + C(A + B)
___
S = (A + B +C )Cout + A B C
12
23
LOGIC OR BOOLEAN ALGEBRA
A SHORT OVERVIEW
OR BOOLEAN ALGEBRA IN A NUTSHELL
24
BOOLEAN ALGEBRA
Logic circuits are the basis for modern digital computer and
other digital systems. To appreciate how digital systems
operate one needs to understand digital logic and Boolean
algebra.
Boolean logic forms the basis for computation in modern
binary computer systems. One can represent any algorithm,
or any electronic computer circuit, using a system of
Boolean equations.
13
25
BOOLEAN ALGEBRA: ITS ROOTS
The Boolean algebra is a brand of mathematics that was
first developed systematically, because of its applications
to logic, by the English mathematician George Boole,
around 1850.
A modern engineering application is to switching, digital
and computer circuit design.
Contributions by Augustus De Morgan (contemporary of
Boole) and by Claude Shannon (1930’ies and 1940’ies)
are also important.
26
BOOLEAN ALGEBRA AND DIGITAL CIRCUITS
The connection between Boolean algebra and switching
circuits has been established by Claude Shannon in the
1930’s.
Boolean algebra is the main analytical tool for the analysis
and synthesis of logic circuits and networks.
Boolean logic
Rules for handling Boolean constants and variables that can
take on 2 values
–True/false; on/off; closed/open; yes/no; 1/0; high/low
(voltage)
–3 fundamental operations: AND, OR and NOT
14
BOOLEAN ALGEBRA: RELEVANCE
In the 1930s, while studying switching circuits, Claude
Shannon observed that one could also apply the rules of
Boole's algebra in this setting, and he introduced switching
algebra as a way to analyze and design circuits by algebraic
means in terms of logic gate.
Shannon already had at his disposal the abstract
mathematical apparatus, thus he cast his switching algebra
as the two-element Boolean algebra.
In circuit engineering settings today, there is little need to
consider other Boolean algebras, thus "switching algebra"
and "Boolean algebra" are often used interchangeably.
BOOLEAN ALGEBRA: RELEVANCE
Efficient implementation of Boolean functions is a
fundamental problem in the design of combinational circuits.
Modern electronic design automation tools for VLSI circuits
often relay on an efficient representation of Boolean
functions like (reduced ordered) binary decision diagrams
(BDD) for logic synthesis and formal verification.
15
29
30
BOOLEAN OPERATORS
• AND
– Result TRUE if and only
if both input operands are true
– C = A B
• OR
– Result TRUE if any input operands
are true
– C = A + B
A B C
0 0 0
0 1 0
1 0 0
1 1 1
A B C
0 0 0
0 1 1
1 0 1
1 1 1
16
31
CMOS IMPLEMENTATION: AND, OR
AND gate OR gate
C = A B C = A + B
32
BOOLEAN OPERATORS
• NOT
– Result TRUE if single input value is
FALSE
– C = A
A C
0 1
1 0
_
A A
Implementation
17
33
BOOLEAN OPERATORS: EXCLUSIVE-OR
• EXCLUSIVE-OR
– Result TRUE if either A or B is
TRUE but not both
– C = A ⊕ B
– Can be derived from OR, AND and NOT
•
A xor B equals A or B but not both A and B
•
A xor B = either A and not B or B and not A
The XOR is not a fundamental Boolean operator, it can
rather be considered as one of the (simplest) Boolean
functions.
Logic circuit families usually offer XOR „gates” too.
A B C
0 0 0
0 1 1
1 0 1
1 1 0 A ⊕ B = (A + B) ( A B )
A ⊕ B = (A B ) + ( B A )
CMOS IMPLEMENTATION: XOR
Vdd Vdd
A
B
A B
A
B
A B
_______
_____ _ _
Note A B = A B = A B + A B (!)
18
35
NOTATIONS: ENGINEERING VERSUS
MATHEMATICS
In electrical engineering and digital electronics the dot (),
the plus sign (+), and the overline (bar) are used for the
logic operations of AND, OR and NOT respectively.
In mathematics, more specifically in mathematical logic
(Boolean) algebra the respective notations are
(conjunction),
(disjunction), and
(negation).
36
AND, OR, NOT, NAND, NOR All logic functions and circuits can be described in terms of the
three fundamental elements.
While the NOT, AND, OR functions have been designed as
individual circuits in many circuit families, by far the most
common functions realized as individual circuits are the NAND
and NOR circuits. A NAND can be described as equivalent to
an AND element driving a NOT element. Similarly, a NOR is
equivalent to an OR element driving a NOT element.
The reason for this strong bias favouring inverting outputs is
that the transistor, and the vacuum tube which preceded it, are
by nature inverters or NOT-type devices when used as signal
amplifiers. Electric and electronic switches (gates) do not
readily perform the OR and AND logic operations, but most
commercially available gates do perform the combined
operations AND-NOT (NAND) and OR-NOT (NOR).
19
37
BOOLEAN POSTULATES
1. Boolean algebra is defined on a set of two-valued
elements
2. Each element of the set has its complementary also
belonging to the set
3. Logic operations: conjunction (logic AND) and
disjunction (logic OR)
4. Logic operations are commutative, associative, and
distributive
5. Special elements of the set are the unity (its value is
always 1) and the zero (its value is always 0)
38
MANIPULATE EXPRESSIONS
BOOLEAN MINIMIZATION Need a way to manipulate expressions.
Rules of ‘adding’, ‘multiplying’ plus associative, distributive laws
etc. The rules are very similar to basic algebra.
One can transform one Boolean expression into an equivalent
expression by applying the postulates the theorems of Boolean
algebra. This is important if one wants to convert a given
expression to a canonical form (a standardized form) or if one
wants to minimize the number of literals (asserted or negated
variables) or terms in an expression. Minimizing terms and
expressions can be important because electrical circuits often
consist of individual components that implement each term or
literal for a given expression. Minimizing the expression allows
the designer to use fewer electrical components and, therefore,
can reduce the cost of the system.
20
39
BOOLEAN THEOREMS
commutative law
A • B = B • A
A + B = B + A
associative law
A • (B • C) = (A • B) • C = A • B • C
A + (B + C) = (A + B)+ C = A + B + C
distributive law
A • (B + C) = A • B + A • C
A + (B • C) = (A + B) • (A + C)
The theorems above appear in pairs. Each pair form a dual.
40
DE MORGAN’S THEOREM
De Morgan’s theorem occupies an important place in the logic
(Boolean) algebra
–––––– — —
A + B = A • B
––––– — —
A • B = A + B
In logic, De Morgan’s laws (or theorem) are rules in formal
logic relating pairs of dual logic operators in a systematic
manner expressed in terms of negation. De Morgan’s
theorem may be applied to the negation of a disjunction or to
the negation of a conjunction in all part of a formula.
21
41
DE MORGAN’S THEOREM
Negation of a disjunction
–––––– — —
A + B = A • B
Since two things are false, it’s also false that either of them is
true.
Negation of conjunction
––––– — —
A • B = A + B
Since it is false that two things together are true, at last one of
them should be false.
42
DE MORGAN’S THEOREM ON THE K-MAP –––––– — —
A + B = A • B
––––– — —
A • B = A + B
Representation of De Morgan’s theorem on the Karnaugh
map or Veitch diagram.
22
43
DE MORGAN’S THEOREM
De Morgan’s formulation of his theorem influenced the
algebraization of logic undertaken by Boole, which cemented
De Morgan’s claim to the find, although a similar observation
was made by Aristotle and was known to Greek and Medieval
logicians, e.g. to William Ockham (1325), the great medieval
scholastic philosopher.
In electrical engineering context the negation operator can be
written as an overline (bar) above the terms to be negated.
In the originate the mnemonic
”break the line, change the operation”
44
BOOLEAN THEOREMS: DUALITY
The theorems above appear in pairs. Each pair form a dual.
An important principle in the Boolean algebra system is that of
duality. Any valid expression you can create using the
postulates and theorems of Boolean algebra remains
valid if you interchange the operators and constants appearing
in the expression. Specifically, if one exchanges the • (AND)
and + (OR) operators and swaps the 0 and 1 values in an
expression, one will wind up with an expression that obeys all
the rules of Boolean algebra. This does not mean the dual
expression computes the same values, it only means that both
expressions are legal in the Boolean algebra system.
Therefore, this is an easy way to generate a second theorem
for any fact one proves in the Boolean algebra system.
23
45
GENERALIZED DE MORGAN’S
THEOREMS
The De Morgan’s theorem is an important tool in the
analysis and synthesis of digital and logic circuits. Its
generalization to several variables is stated below
_____ _ _ _
A B C ... = A + B + C + ...
________ _ _ _
A + B + C + ... = A B C ...
46
SHANNON’S GENERALIZATION OF
DE MORGAN’S THEOREMS
The De Morgan-Shannon’s theorem refers to the logic or
Boolean functions constructed using logic multiplications
and additions
_____________ _ _ _
f(A, B, C, ..., +, •) = f(A, B, C, ..., •, +)
The negation of the function can be performed by
negating each variable and replacing all logic
summations (ORs) with logic multiplications (ANDs) and
replacing all logic multiplications (ANDs) with logic
summations (ORs).
24
47
SHANNON’S EXPANSION THEOREMS
__
F(X1, X2,…Xn) = X1 F(1,X2,…Xn) + X1 F(0,X2,…Xn)
__
F(X1, X2,…Xn) = X1 + F(0,X2,…Xn) X1 + F(1,X2,…Xn)
Application: decomposition of logic functions to smaller
blocks, or for implementation using MUX based logic cells.
Example:
48
KEY APPLICATION OF
DE MORGAN THEOREM
AND operation using OR and NOT
————
— —
A • B = (A + B)
OR operation using AND and NOT
————
— —
A + B = (A • B)
25
49
LOGIC CIRCUITS IN PRACTICE
Any logic circuit can be implemented using only NAND or
only NOR operations.
In the transistor-transistor-logic (TTL) logic circuit system
which is based on silicon bipolar technology the NAND gate
is the basic element.
In the logic circuit system based on silicon complementary
metal-oxide-semiconductor (CMOS) technology the NOR
gate is (mostly) the basic element.
LOGIC GATES
• Elementary building blocks of logic circuits.
• They implement a basic logic operations.
• Complex logic networks can be implemented by
appropriate interconnection of logic gates.
• However nowadays: use more complex building blocks
and functional elements (complexity: few tens to few
hundred gates), or some kind of programmable logic
devices (complexity up to ten thousand gates or even
more). E. g. the complexity of a 1 digit BCD-to-seven
segment display decoder is about 30 gates, of a 4-bit
ALU is less than 100 gates. Both are available in MSI in
one package.
26
51
IMPLEMENTATION OF
COMBINATIONAL CIRCUITS
Any two-level AND-OR circuit (sum-of-products, SOP) can be
implemented using a two-level NAND-NAND circuit.
Any two-level OR-AND circuit (product-of-sums, POS) can be
implemented using a two-level NOR-NOR circuit.
All these are based on De Morgan’s theorem.
52
LOGICAL SYNTHESIS GUIDED BY
DE MORGAN THEOREM
27
53
BOOLEAN FUNCTIONS
The one- and two-variable operations of Boolean algebra can
be considered as functions of one and two variables,
respectively.
In the case of generalized functions the number of variables is
extended only.
n-variable Boolean or logic function
Z = f(X1, X2, .........Xn)
The particular truth value of Z is defined by the f function.
54
CLASSIFICATION OF BOOLEAN
FUNCTIONS OF TWO VARIABLES
Name of the function f(A,B)
——————————————————————
Logical constants 0, 1
— —
Functions of one variable A, A, B, B
—— ———
AND, OR, NAND, NOR A•B, A+B, A•B, A+B
— — — —
XOR (AB ), XNOR (AB) A B+A B, A B+A B
INHIBITION A B, B A
IMPLICATION A B, B A
28
55
BOOLEAN FUNCTIONS OF TWO VARIABLE
VA
GY 1
A B
0 0
0 1
1 0
1 1
f0
f1
f2
f3
f4
f5
f6
f7
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
f8
f9
f10
f11
f12
f13
f14
f15
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
ÉS ÉS
-NE
M
VA
GY
-NE
M
A AB B
Egyargumentumos
Egyargumentumos
Logikai konstansok
AND
NAND
OR NOR
Boolean constants
One variable
One variable
56
THE 16 POSSIBLE BOLEAN FUNCTINS
OF TWO VARIABLES
29
57
BOOLEAN FUNCTIOS AND OPERATIONS
OF TWO VARIABLES: A SUMMARY
From the 16 possible two-variable Boolean functions
6 can be considered as trivial (2 of them are constants, 4 of them are in fact one-variable functions) From the 10 non-trivial functions 2 (AND and OR) and their complementary (AND-NOT and OR-NOT) as well as the EXCLUSIVE-OR (antivalency) and the EXCLUSIVE-NOR (equivalency) are of significance for the practice.
58
IC IMPLEMENTATION: E.G. 74HC/HCT181
Total 16 arithmetic operations (add, subtract, plus, shift, plus 12 others)
• Total 16 logic operations (XOR, AND, NAND, NOR, OR, plus 11 others)
• Capable of active-high and active-low operation
30
59
WAYS TO DEFINE LOGIC FUNCTIONS
How to define a logic function?
There are several possible ways to do it.
Truth table or its special forms, like
- characteristic number
- canonical (algebraic) forms
(These are unique definitions – with some conditions)
Developed in 1854 by George Boole
Further developed by Claude Shannon (Bell Labs)
Outputs are computed for all possible input
combinations
Graphic representation with Karnaugh map
(This one is unique too)
So called algebraic form, which is not unique.
Some appropriate function-definition language, like VHDL
60
DEFINITION OF A LOGIC FUNCTIONS
BY ITS 1 VALUES
List the indices of those variable combinations to which a 1
value of the function belongs to.
This kind of definition also needs the agreement on the
weights of the variables.
This definition is known as (extended) SOP (sum-of-products)
or disjunctive canonical form.
This definition is also unique similarly to the characteristic
number.
31
61
THE SOP FORM OF THE MAJORITY GATE
• The (extended) SOP form for the 3-input majority gate is:
• M = m3 + m5 +m6 +m7 = 3(3, 5, 6, 7)
• Each of the 2n terms are called minterms, running from 0 to
2n – 1
• Note the relationship between minterm number and Boolean
value.
Two-level AND-OR
implementation:
CMOS (SSI)
implementation: 4062
logic dual majority gate
62
THE CONJUNCTIVE CANONICAL FORM
(EXTENDED) PRODUCT-OF-SUMS
There exist an other canonical form, the conjunctive
canonical form, or the (extended) product-of-sums (POS)
form.
This is also unique.
The two canonical forms are equivalent and can be
transformed into each other using the De Morgan theorem.
32
63
DEFINITION OF A LOGIC FUNCTION
BY ITS MINTERMS
Ai
Bi
Ci-1
Di
i
0
1
2
3
4
5
6
7
0
0
0
0
111
1
0
0
00
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
00
(4) (2) (1)
Ci
0
0
0
1
11
0
1
Di= (1,2,4,7)
Ci = (3,5,6,7)
Example: 1-bit full adder
Si = m13 + m2
3 + m43 + m7
3 =
= Σ3(1,2,4,7)
_ _ E. g. m2
3 = A B C, etc.
Si
Si
64
DEFINITION OF THE FUNCTION BY
CHARACTERISTIC NUMBER
Defining a logic function by its characteristic
number is unanimous only if the weights of
the independent variables are fixed
beforehand.
33
65
THE DISJUNCTIVE CANONICAL FORM
(EXPANDED) SUM-OF-PRODUCTS
The minterms of all n-variable functions are n-literal products
Any logic function of n-variables can be defines by a sum of
n-variable minterms (sum of products, SOP)
This is unambiguous only if the weighing of the independent
variables is given.
Since logic summing is disjunction, this form is also known as
disjunctive canonical form of a logic function.
The corresponding SOP is termed as expanded sum-of-
products form
66
EXAMPLE:
THE TWO CANONICAL FORMS OF XOR
The (trivial) extended SOP form (disjunctive canonical form) of
the XOR function (F(A,B) = A B is
_ _
F = A B + A B = Σ2 (1,2)
The extended POS form (conjunctive canonical form) of the
same function is
_ _
F = (A + B) (A + B) = Π2 (0,3)
34
67
CANONICAL FORMS, MINTERMS, AND
PRIME IMPLICANTS
The ”standard sum-of-products form” is also known as the
”minterm canonical form” or ”canonic sum function”. It is a
”sum” (OR) of minterms.
A minterm is also known as the ”standard product” or
”canonic product term”. This is a term where each variable is
used once and once only.
A ”prime implicant” is an implicant of a function which does
not imply any other implicant of the function.
68
THE END